[ January 23, 2005 ]
List of palindromic areas of primitive Pythagorean triangles
Zakir Seidov (website)
“ I saw before your Palindromic Pythagorean Triples,
and it inspired me to look for palindromic areas.
I've just sent to OEIS the 'all I know' cases of
palindromic areas of primitive Pythagorean triangles.
Hope it'd be interesting to visitors of your great site.”
{area, leg a, leg b, hypo c}
{6, 3, 4, 5}, Primitive!
{63336, 336, 377, 505}, Primitive!
{474474, 156, 6083, 6085},Primitive!
{666666, 693, 1924, 2045}, Primitive!
{4053504, 2688, 3016, 4040},
{4244424, 408, 20806, 20810},
{4383834, 1443, 6076, 6245}, Primitive!
{42066024, 8008, 10506, 13210},
{42666624, 5544, 15392, 16360},
{43177134, 3476, 24843, 25085}, Primitive!
{610262016, 12432, 98176, 98960},
{6390000936, 82214, 155448, 175850},
{48576067584, 23168, 4193376, 4193440},
{460962269064, 81073, 11371536, 11371825}, Primitive!
{654513315456, 304928, 4292904, 4303720},
{60490233209406, 5390853, 22441804, 23080205}, Primitive!

Note that we now have eight new cases of pal_areas
of primitive Pythagorean triangles (PPTs) !
( primitive means "with no common factors" )
ID Number: A101439
URL: https://oeis.org/A101439
Sequence: 63336,474474,666666,4383834,43177134
Name: Areas of primitive Pythagorean triangles which are palindromes.
Comments: Other triangles are: n=1, a=336, b=377, c=505; n=2, a=156, b=6083,
c=6085; n=4, a=1443, b=6076, c=6245; n=5, a=3476, b=24843, c=25085.
What is the next case?
Example: 666666 is a member, as it is a palindromic number, and is area of
primitive Pythagorean triangle with legs a=693, b=1924, and
hypotenuse c=2045.
Keywords: more,nonn,base,new
Offset: 1
Author(s): Zak Seidov (seidovzf(AT)yahoo.com), Jan 18 2005
ID Number: A101450
URL: https://oeis.org/A101450
Sequence: 6,63336,474474,666666,4053504,4244424,4383834,42066024,
42666624,43177134,610262016,6390000936,48576067584,
460962269064,654513315456,60490233209406
Name: Areas of (notnecessarilyprimitive) Pythagorean triangles which
are palindromes.
Comments: Compare areas of primitive Pythagorean triangles which are
palindromes, A101439. Are these lists full? What are the next cases?
Example: 666666 is a member, as it is a palindromic number, and is area of
Pythagorean triangle with legs a=693,b=1924, and hypotenuse c=2045.
See also: Cf. A101439.
Keywords: base,more,nonn,new
Offset: 0
Author(s): Zak Seidov (seidovzf(AT)yahoo.com), Jan 19 2005

Did you know that 474474 (156^2 + 6083^2 = 6085^2)
is also the product of three consecutive numbers
namely 77 x 78 x 79.
Note that in the 2nd case hypotenuse 505 is also palindromic!
From Mike Keith's webpage The Number of the Beast
There are only two known Pythagorean triangles
whose area is a repdigit number:
(3, 4, 5) with area 6
(693, 1924, 2045) with area 666666
It is not known whether there are any others, though a computer
search has verified that there are none with area less than 10^{40}.
[see J. Rec. Math, 26(4), Problem 2097 by Monte Zerger]
666666_{10} remains palindromic when converted to hexadecimal base i.e., A2C2A_{16}
On the internet we can consult a general list with 'leg b'
up to 10000 : Pythagorean Triple Table by Michael Somos
